Variational Dropout and the Local Reparameterization Trick

We investigate a local reparameterizaton technique for greatly reducing the variance of stochastic gradients for variational Bayesian inference (SGVB) of a posterior over model parameters, while retaining parallelizability. This local reparameterization translates uncertainty about global parameters into local noise that is independent across datapoints in the minibatch. Such parameterizations can be trivially parallelized and have variance that is inversely proportional to the minibatch size, generally leading to much faster convergence. Additionally, we explore a connection with dropout: Gaussian dropout objectives correspond to SGVB with local reparameterization, a scale-invariant prior and proportionally fixed posterior variance. Our method allows inference of more flexibly parameterized posteriors; specifically, we propose variational dropout, a generalization of Gaussian dropout where the dropout rates are learned, often leading to better models. The method is demonstrated through several experiments

Deep Kernels for Optimizing Locomotion Controllers

Sample efficiency is important when optimizing parameters of locomotion controllers, since hardware experiments are time consuming and expensive. Bayesian Optimization, a sample-efficient optimization framework, has recently been widely applied to address this problem, but further improvements in sample efficiency are needed for practical applicability to real-world robots and high-dimensional controllers. To address this, prior work has proposed using domain expertise for constructing custom distance metrics for locomotion. In this work we show how to learn such a distance metric automatically. We use a neural network to learn an informed distance metric from data obtained in high-fidelity simulations. We conduct experiments on two different controllers and robot architectures. First, we demonstrate improvement in sample efficiency when optimizing a 5-dimensional controller on the ATRIAS robot hardware. We then conduct simulation experiments to optimize a 16-dimensional controller for a 7-link robot model and obtain significant improvements even when optimizing in perturbed environments. This demonstrates that our approach is able to enhance sample efficiency for two different controllers, hence is a fitting candidate for further experiments on hardware in the future.Comment: (Rika Antonova and Akshara Rai contributed equally

Bayesian Deep Net GLM and GLMM

Deep feedforward neural networks (DFNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a DFNN. The consideration of neural networks with random effects is not widely used in the literature, perhaps because of the computational challenges of incorporating subject specific parameters into already complex models. Efficient computational methods for high-dimensional Bayesian inference are developed using Gaussian variational approximation, with a parsimonious but flexible factor parametrization of the covariance matrix. We implement natural gradient methods for the optimization, exploiting the factor structure of the variational covariance matrix in computation of the natural gradient. Our flexible DFNN models and Bayesian inference approach lead to a regression and classification method that has a high prediction accuracy, and is able to quantify the prediction uncertainty in a principled and convenient way. We also describe how to perform variable selection in our deep learning method. The proposed methods are illustrated in a wide range of simulated and real-data examples, and the results compare favourably to a state of the art flexible regression and classification method in the statistical literature, the Bayesian additive regression trees (BART) method. User-friendly software packages in Matlab, R and Python implementing the proposed methods are available at https://github.com/VBayesLabComment: 35 pages, 7 figure, 10 table